Physical Combinatorics

物理组合学

基本信息

批准号：
13304010
负责人：
MIWA Tetsuji
金额：
$ 17.72万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

The main research results of the project consist of the following 5 parts.(i)We defined a filtration in the space of conformal coinvariants by using the degree defined by the representation at the infinity. We obtained a formula to represent the character of the associated gradedspace in terms of the Kostka polynomials. In this formula, we use the character of coinvariants for the fusion products. The obtained formulasare of fermionic type. We also obtained a bosonic formulas by solving a recursion relation.(ii)We constructed a basis of the space of symmetric polynomials satisfying a certain zero condition called the wheel condition by using the Jack and the Macdonald polynomials. This space is nothing but the minimal subrepresentation of the polynomial representation of the double affine Hecke algebra when it is reducible at the special values of the parameters.(iii)We realized the space of solutions to the system of difference equations which characterize the form factors of integrable quantum field theory, as an infinite dimensional homogeneous space in the representation theory of the quantum groups.(iv)We constructed a monomial basis of the minimal representations of the Virasoro algebra by using the Fourier components of the primary field and the quadratic relations satisfied by them.(v)Formulas in $n$-fold integrals for the $n$-point correlation functions of quantum spin chains are knwon. We obtained an algebraic formula without integrations by solving the qKZ difference equation. We used the transfer matrix with an auxiliary space of continuous dimensions. In the case of the XYZ model, we need the expression for the trace in Sklyanin's algebra. We proved that the calculation of the trace reduces to 7 elements in the algebra, and expressed thier traces by using elliptic theta functions.

该项目的主要研究结果包括以下5个部分。（i）我们使用Infinity的代表定义的程度定义了共同变量空间中的过滤。我们获得了一个公式，可以用科斯特卡多项式来表示相关的分级空间的特征。在此公式中，我们将共同变量的特征用于融合产品。获得的典型类型的公式。我们还通过求解递归关系获得了骨气公式。（ii）我们通过使用Jack和MacDonald多项式构建了满足某些零条件的对称多项式空间的基础。这个空间不过是在参数的特殊值上还可以降低双仿射代数的多项式表示的最小亚代表性。（iii）我们意识到差异方程式的解决方案的空间，这些方程式的空间，这些方程式的差异量子理论的形式表征了一个无限的量子量化量的量子，是一个无限的量子构造的量子，是一个量子构成的量子构造的代表，是一定构建了一定的代表。 Virasoro代数的最小表示的单一基础，使用主要磁场的傅立叶组成部分和它们满足的二次关系。（v）$ n $ fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-fold-point相关函数的量子旋转链的函数是knwon。我们通过求解QKZ差异方程来获得一个无需集成的代数公式。我们使用了带有连续尺寸的辅助空间的转移矩阵。在XYZ模型的情况下，我们需要Sklyanin代数中的痕迹的表达式。我们证明了迹线的计算将代数中的7个元素还原为7个元素，并通过使用椭圆形theta函数表达了THIR痕迹。